Fluid Mechanics
 Liquids and gases have the ability to flow
 They are called fluids
 There are a variety of “LAWS” that fluids obey
 Need some definitions
Fluid Mechanics
 Fluid Mechanics: the study of forces that develop when
an object moves through a fluid medium.
 Two fluids are of interest
– Water
– Air
Fluid forces
 In some cases, fluid forces have little effect on an
object’s motion (e.g., shotput)
 In other cases, fluid forces are significant
– badminton, baseball, swimming, cycling, etc.
 Three major fluid forces are of interest:
– Buoyancy
– Drag
– Lift
Drag and Lift
 The drag force acts in a direction that is opposite of
the relative flow velocity.
– Affected by cross-section area (form drag)
– Affected by surface smoothness (surface drag)
 The lift force acts in a direction that is
perpendicular to the relative flow.
– The lift force is not necessarily vertical.
Drag
 Resistive force acting on a body moving through a
fluid (air or water). Two types:
 – Surface drag: depends mainly on smoothness of surface
of the object moving through the fluid.

shaving the body in swimming; wearing racing suits in skiing and
speed skating.
 – Form drag: depends mainly on the cross-sectional area of
the body presented to the fluid


bicyclist in upright v. crouched position
swimmer: related to buoyancy and how high the body sits in the
water.
– When would you want to increase drag?
Lift
 Represents a net force that acts perpendicular to
the direction of the relative motion of the fluid;
 Created by different pressures on opposite sides of
an object due to fluid flow across the object
– example: Discus face turns downward
 Bernoulli’s principle: velocity is inversely
proportional to pressure.
– Fast relative velocity lower pressure
– Slow relative velocity higher pressure
Examples
 Baseball: curveball,
 Golf: slice,
 Tennis: top-spin forehand, Slice
 Soccer: Curved corner kick
 Volleyball: top-spin jump serve
The Magnus Effect
 The Magnus effect describes the curved path that is
observed by spinning projectiles.
– Explained by Bernoulli’s principle and the pressure
differences caused by relative differences in a moving
fluid.
Bernoulli’s Principle
 Faster Airflow
Lower Pressure
 Slower Airflow Higher Pressure
Buoyancy
 Associated with how well a body floats or how
high it sits in the fluid.
 Archimede’s principle: any body in a fluid
medium will experience a buoyant force equal
to the weight of the volume of fluid which is
displaced.
– Example: a boat on a lake. A portion of the
boat is submerged and displaces a given volume
of water. The weight of this displaced water
equals the magnitude of the buoyant force
acting on the boat.
Buoyancy
 The boat will float if its weight in air is less than or equal
to the weight of an equal volume of water.
 Buoyancy is closely related to the concept of
density.
 Density = mass/volume
 Specific Gravity = Body Weight/Displaced
water weight
Buoyancy
 A ratio of greater than 1 exhibits that the body will
sink because the body weight is more than the
displaced water.
 A ratio of less than 1 designate that the body will
float because the displaced water weight is more
than the weight of body.
Example: Underwater weighing
 Body composition assessment using the underwater
weighing technique is common application of Archimede’s
principle.
– Human body is composed of varying amounts of muscle,
bone, and fat.
– Densities of:



Fat: 0.95 g/cm3
Muscle: 1.05-1.10 g/cm3
Bone: 1.4-1.9 g/cm3
– Underwater weighing provides a direct estimate of
average body density. Prediction equations then allow for
estimation of %fat and %lean body mass.
Center of buoyancy
 Increased tilt in water results in greater form drag!
This decreases efficiency!
 Research has shown that men have a greater drag
than women. This creates a greater “feet sinking
torque”.
 It has been suggested that this is a bigger problem
for men than for women.
Density & Pressure
 Density : Regardless of form (solid, liquid, gas) we
can define how much mass is squeezed into a
particular space.
 Pressure : A measure of the amount of force
exerted on a surface area.
Pressure in a Fluid
 The pressure is just the weight of all the fluid above
you
 Atmospheric pressure is just the weight of all the air
above on area on the surface of the earth
 In a swimming pool the pressure on your body surface
is just the weight of the water above you (plus the air
pressure above the water)
Pressure in a Fluid
 So, the only thing that counts in fluid pressure is the
gravitational force acting on the mass ABOVE you
 The deeper you go, the more weight above you and the
more pressure
 Go to a mountaintop and the air pressure is lower
Pressure Concept
Pressure acts
perpendicular to the
surface and increases
at greater depth.
Buoyancy
Net upward
force is called
the buoyant
force!!!
Easier to lift a
rock in
water!!
Displacement of Water
The amount of
water displaced
is equal to the
volume of the
rock.
Archimedes’ Principle
 An immersed body is buoyed up by a force equal to the
weight of the fluid it displaces.
 If the buoyant force on an object is greater than the
force of gravity acting on the object, the object will
float
 The apparent weight of an object in a liquid is
gravitational force (weight) minus the buoyant force
Flotation
A floating
object
displaces a
weight of
fluid equal to
its own
weight.
Flotation Example
Principles of Fluid Flow
 The continuity
equation results
fromconservation of
mass.
 Continuity equation:
A1v1 = A2v2
Area x speed in
region 1 = area x
speed in region 2
Bernoulli’s Principle
Flow is
faster
when the
pipe is
narrower
Bernoulli’s Principle
When the
speed of a
fluid
increases,
internal
pressure in
the fluid
decreases.
Principles of Fluid Flow
 The speed of fluid
flowdepends on
crosssectionalarea.
 Bernoulli’s principle
states that the
pressurein a fluid
decreases as the fluid’s
velocity increases.
Factors to be Controlled for Reducing
Water Resistance
 Waves
 Eddies
 Cavitation
 Skin Friction (Surface Drag)
 Starting and stopping force
 Force applied on unproductive angle
 Form drag
 Internal Resistance